I have been struggling with this problem:
Knights always tell the truth but knaves never tell the truth. In a group of three
individuals (who we will label as N1, N2, and N3) each is either a knight or a knave. Each
makes a statement:
N1: “We are all three knaves.”
N2: “Two of us are knaves and one of us is a knight."
N3: “I am a knight and the other two are knaves.”
Which are knights and which are knaves? Explain your reasoning.
I think that N1 is a Knave because at least one of them should be a Knight, however I am not able to determine if the other two are Knights or Knaves, because I think that they could both be telling the truth, however that would lead to a contradiction.
Best Answer
if $N_3$ were a knight, then there are two knaves and a knight, but that would mean that $N_2$ tells the truth and hence he is a knight, which means that there are at least two knight or at most one knave. A contradiction. Hence $N_3$ is a knave. Clearly, $N_1$ is also a knave, for if he were a knight, then everybody would be a knave. A contradiction. Now as the first is a knave, then he lies, and hence not all of them are knaves and hence $N_2$ is a knight. Indeed, what $N_2$ says is consistent.